diff --git a/backend/sftp/sftp.go b/backend/sftp/sftp.go
index 1fe1553f7..176e24dd9 100644
--- a/backend/sftp/sftp.go
+++ b/backend/sftp/sftp.go
@@ -125,12 +125,6 @@ type Object struct {
 	sha1sum *string     // Cached SHA1 checksum
 }
 
-// ObjectReader holds the sftp.File interface to a remote SFTP file opened for reading
-type ObjectReader struct {
-	object   *Object
-	sftpFile *sftp.File
-}
-
 // readCurrentUser finds the current user name or "" if not found
 func readCurrentUser() (userName string) {
 	usr, err := user.Current()
@@ -877,15 +871,49 @@ func (o *Object) Storable() bool {
 	return o.mode.IsRegular()
 }
 
+// objectReader represents a file open for reading on the SFTP server
+type objectReader struct {
+	sftpFile   *sftp.File
+	pipeReader *io.PipeReader
+	done       chan struct{}
+}
+
+func newObjectReader(sftpFile *sftp.File) *objectReader {
+	pipeReader, pipeWriter := io.Pipe()
+	file := &objectReader{
+		sftpFile:   sftpFile,
+		pipeReader: pipeReader,
+		done:       make(chan struct{}),
+	}
+
+	go func() {
+		// Use sftpFile.WriteTo to pump data so that it gets a
+		// chance to build the window up.
+		_, err := sftpFile.WriteTo(pipeWriter)
+		// Close the pipeWriter so the pipeReader fails with
+		// the same error or EOF if err == nil
+		_ = pipeWriter.CloseWithError(err)
+		// signal that we've finished
+		close(file.done)
+	}()
+
+	return file
+}
+
 // Read from a remote sftp file object reader
-func (file *ObjectReader) Read(p []byte) (n int, err error) {
-	n, err = file.sftpFile.Read(p)
+func (file *objectReader) Read(p []byte) (n int, err error) {
+	n, err = file.pipeReader.Read(p)
 	return n, err
 }
 
 // Close a reader of a remote sftp file
-func (file *ObjectReader) Close() (err error) {
+func (file *objectReader) Close() (err error) {
+	// Close the sftpFile - this will likely cause the WriteTo to error
 	err = file.sftpFile.Close()
+	// Close the pipeReader so writes to the pipeWriter fail
+	_ = file.pipeReader.Close()
+	// Wait for the background process to finish
+	<-file.done
 	return err
 }
 
@@ -919,10 +947,7 @@ func (o *Object) Open(options ...fs.OpenOption) (in io.ReadCloser, err error) {
 			return nil, errors.Wrap(err, "Open Seek failed")
 		}
 	}
-	in = readers.NewLimitedReadCloser(&ObjectReader{
-		object:   o,
-		sftpFile: sftpFile,
-	}, limit)
+	in = readers.NewLimitedReadCloser(newObjectReader(sftpFile), limit)
 	return in, nil
 }